On the random greedy F-free hypergraph process

Deryk Osthus, Daniela Kuhn, Amelia Taylor

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
206 Downloads (Pure)

Abstract

Let $F$ be a strictly $k$-balanced $k$-uniform hypergraph with $e(F)\geq |F|-k+1$ and maximum co-degree at least two.
The random greedy $F$-free process constructs a maximal $F$-free hypergraph as follows.

Consider a random ordering of the hyperedges of the complete $k$-uniform hypergraph $K_n^k$ on $n$ vertices.
Start with the empty hypergraph on $n$ vertices. Successively consider the hyperedges $e$ of $K_n^k$ in the given ordering and add $e$ to the
existing hypergraph provided that $e$ does not create a copy of $F$.
We show that asymptotically almost surely this process terminates at a hypergraph with $\tilde{O}(n^{k-(|F|-k)/(e(F)-1)})$ hyperedges. This is best possible up to logarithmic factors.
Original languageEnglish
Pages (from-to)1343-1350
JournalSIAM Journal on Discrete Mathematics
Volume30
Issue number3
Early online date12 Jul 2016
DOIs
Publication statusPublished - 2016

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